Question

The U.S. Environmental Protection Agency set a maximum contaminant level (MCL) for tetrachloroethylene (TCE, C2Cl4) in drinking water of 0.005 ppm (by mass). If the water in your home contains 13.0 percent of the allowable MCL, what is the molarity of TCE in your home?

Answer 1

`3.85*10^(-9)M.`

Step-by-step explanation:

1. Find how much TCE there's in the water in your home.

If the water contains 13.0 percent of the allowable MCL, then the relative level of TCE by mass is given by the following equation:

`0.13*0.005ppm=0.00065ppm`.

2. Find the molarity.

Formula of molarity:
`M=(n)/(v)`, where n is the amount of moles of the solute and v are the liters of the solution.

Taking the fact that we have relative values of amounts of the substance, we may set up an example calculation with arbitrary values to find a solution.

Let's say that you take a 1 liter bottle and fill it out with water from your house. Let's solve the problem.

a. Finding the liters of solution.

In this case, we set the number of liters previously, it's 1.

b. Finding the moles of solute.

If the amount of water in the bottle is 1 liter, and the density if water is
`1g/cm^(3)`, then we need to convert the liters to
`cm^(3)` and calculate the mass of water.

`1L=1000mL=1000cm^(3)`

Given the density of water (
`1g/cm^(3)`), the mass of
`1000cm^(3)` is
`1000g`.

Now, the mass of TCE in 1000g of water is:

`1000g*0.00065ppm=1000g*(0.00065)/(1000000) =6.5*10^(-7) g`.

Looking at the formula of TCE (
`C_(2) Cl_(4)`) the amount of carbon atoms is 2, and the amount of chlorine atoms is 4. Hence, the molar mass of this compound is given by:

`(2 atoms)(12.011u)+(4 atoms)(35.45u)=165.82g/mol.`

This means that the mass of a mole of
`C_(2) Cl_(4)` is 168.82 grams.

Now, to find out how many moles of TCE we have in the bottle of 1L, set up and solve a rule of 3. Do it on the following fashion:

168.82g ------------------ 1 mole

6.5*10^-7 g -------------- x moles

`x=((6.5*10x^(7) *1))/(168.82)=3.8503*10^(9) (moles)`

Substitute the values in the formula of molarity:

`M=(3.8503*10^(-9) moles)/(1L) =3.8503*10^(-9)M.`

3. Express your result.

`3.85*10^(-9)M.`